Lecture 15: Two Sample Hypothesis Tests

class: center, top, .title-slide, title-slide

# Lecture 15: Two Sample Hypothesis Tests
## STAT 324
### Ralph Trane
### University of Wisconsin–Madison<br><br>
### Spring 2020

---

layout: true

# Two Independent Samples Hypothesis Test

---

The horned lizard Phrynosoma mcalli is named for the fringe of spikes around the back of the head. It was thought that the spikes may provide the lizard protection from its primary predator, the loggerhead shrike, Lanius ludovicanus, though there was not much existing quantitative evidence to support this. Researchers were interested in comparing two populations: the population of dead lizards known to be killed by shrikes, and the population of live lizards from the same geographic location. Random samples were taken from each population. The longest spike was measured on each sampled lizard, in mm.

---

The fundamental question: is there, overall, a difference between the longest spike in the two populations?

In terms of means: is `$\mu_\text{dead} = \mu_\text{alive}$` or not?

Some data:

```r
DT::datatable(lizards, options = list(pageLength = 4))
```

<div id="htmlwidget-af87021d22a026169a29" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-af87021d22a026169a29">{"x":{"filter":"none","data":[["1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19","20","21","22"],["dead","dead","dead","dead","dead","dead","dead","dead","dead","dead","alive","alive","alive","alive","alive","alive","alive","alive","alive","alive","alive","alive"],[17.65,20.83,24.59,18.52,21.4,23.78,20.36,18.83,21.83,20.06,23.76,21.17,26.13,20.18,23.01,24.84,19.34,24.94,27.14,25.87,18.95,22.61]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>group<\/th>\n      <th>size<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"pageLength":4,"columnDefs":[{"className":"dt-right","targets":2},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[4,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>

---

The fundamental question: is there, overall, a difference between the longest spike in the two populations?

In terms of means: is `$\mu_\text{dead} = \mu_\text{alive}$` or not?

.pull-left[

```r
ggplot(lizards,
       aes(x = group, y = size)) + 
  geom_boxplot(aes(fill = group),
               alpha = 0.2) + 
  geom_hline(data = lizards %>% 
               group_by(group) %>% 
               summarize(mean = mean(size)),
             aes(yintercept = mean, color = group)) + 
  geom_jitter(height = 0, width = 0.2, 
              aes(color = group)) +
  labs(color = "", fill = "")
```
]

.pull-right[
<img 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" 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]

Are the lines so far apart that we reject the idea that the underlying true means are the same?

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Since `$\bar{X}_\text{dead}$` is expected to be close to `$\mu_\text{dead}$`, and `$\bar{X}_\text{alive}$` is expected to be close to `$\mu_\text{alive}$`, `$\bar{X}_\text{alive} - \bar{X}_\text{dead}$` is expected to be close to `$\mu_\text{alive} - \mu_\text{dead}$`.

We can rephrase the question in terms of hypotheses:

`$$H_0: \mu_\text{alive} - \mu_\text{dead} = 0 \qquad \text{vs.} \qquad H_A: \mu_\text{alive} - \mu_\text{dead} \neq 0$$`

So the question is, is our observed difference in averages ( `$\bar{X}_\text{alive} - \bar{X}_\text{dead}$` ) so far from `$0$` that we no longer think that `$\mu_\text{alive} - \mu_\text{dead} = 0$` (i.e. we reject the idea that the means are the same)?

How would we go about answering this question?

---

**IF** `$\bar{X}_\text{alive} \sim N$` and `$\bar{X}_\text{dead} \sim N$`, then `$\bar{X}_\text{alive} - \bar{X}_\text{dead} \sim$`
--
 `$N$`.

**IF** `$H_0$` is true, then `$E(\bar{X}_\text{alive} - \bar{X}_\text{dead}) = E(\bar{X}_\text{alive}) - E(\bar{X}_\text{dead}) = \mu_\text{alive} - \mu_\text{dead} =$`
--
 `$0$`.

So, **IF** `$H_0$` is true, then `$\bar{X}_\text{alive} - \bar{X}_\text{dead} \sim N(0, ??)$`.

**IF** the two samples are independent of each other, `$\bar{X}_\text{alive}$` is independent of `$\bar{X}_\text{dead}$`, so

`$$\text{Var}(\bar{X}_\text{alive} - \bar{X}_\text{dead}) = \text{Var}(\bar{X}_\text{alive}) + \text{Var}(\bar{X}_\text{dead}) = \frac{\sigma^2_\text{alive}}{n_\text{alive}} + \frac{\sigma^2_\text{dead}}{n_\text{dead}}$$`

So, **IF** `$H_0$` is true, then `$\bar{X}_\text{alive} - \bar{X}_\text{dead} \sim N\left(0, \frac{\sigma^2_\text{alive}}{n_\text{alive}} + \frac{\sigma^2_\text{dead}}{n_\text{dead}}\right)$`.

---

So, how do we judge if what we see is so far from the null hypothesis that we decide to reject it?

By finding the probability of observing something more extreme if we were to repeat the experiment, **assuming the null hypothesis is true**!

**IF** `$H_0$` is true, **and we know `$\sigma_\text{alive}, \sigma_\text{dead}$`**, this is pretty straight forward:

- look at the curve that is the distribution of the difference `$\bar{X}_\text{alive} - \bar{X}_\text{dead}$`, i.e. `$N\left(0, \frac{\sigma^2_\text{alive}}{n_\text{alive}} + \frac{\sigma^2_\text{dead}}{n_\text{dead}}\right)$`.

- using quantiles:
    - find quantiles that cut-off `$\alpha/2$` on each side.
    - reject if observed value of the difference is outside the cut-offs

- using p-value:
    - find probability of something "more extreme"
    - reject if smaller than `$\alpha$`

---

Using quantiles: reject if outside of dotted lines that cut-off `$\alpha/2$` on each side.

---

Using p-value: reject if area outside dotted lines is smaller than `$\alpha$`

---
 
Problem: we never know `$\sigma_\text{dead}, \sigma_\text{alive}$`!!

In the one sample case, we got around this by considering `$\frac{\bar{X} - \mu_0}{\widehat{\text{SD}}(\bar{X})} = \frac{\bar{X} - \mu_0}{s/\sqrt{n}}$`, which we know is `$t_{n-1}$`.

In the two sample case, we will use

$$
  T = \frac{V - v_0}{\widehat{\text{SD}}(V)},
$$

where `$V = \bar{X}_\text{alive} - \bar{X}_\text{dead}$`, and (in the most general case)

`$$\widehat{\text{SD}}(V) = \sqrt{s^2_\text{alive}/n_\text{alive} + s^2_\text{dead}/n_\text{dead}}$$`

As usual, **IF** `$V \sim N$`, and `$H_0: v = v_0$`, then  `$T \sim t_\text{some appropriate df}$`. Things get a bit more tricky here, though, as deciding the approriate df is not trivial.

---

In general, two scenarios:

**Scenario 1**: `$\sigma_1^2 = \sigma_2^2$`.

When this is the case, we replace both by a common number, `$\sigma_\text{pooled}^2$` (or simply `$\sigma^2_p$` for convenience).

Adding this extra bit of information means we can do slightly better in trying to estimate the variance in the two groups. Our best guess for the pooled variance is

`$$\hat{\sigma}^2_p = s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2-1)s_2^2}{n_1 + n_2 - 2}$$`

---

`$$\hat{\sigma}^2_p = s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2-1)s_2^2}{n_1 + n_2 - 2}$$`

Intuition:

* this is a *weighted average* of our two best guesses

* we have a best guess for group 1, best guess for group 2, so surely the "truth" must be somewhere between the two.

* the group with more data (i.e. more information) gets more weight

* if the means in the two groups were the same, the pooled standard deviation is actually the same as just treating the two groups as one.
    - cannot do this when means are different because of definition of standard deviation

We now have that `$\text{Var}(V) = \frac{s_p^2}{n_1} + \frac{s_p^2}{n_2} = s_p^2 (1/n_1 + 1/n_2)$`, and our test statistic will follow a `$t_{n_1+n_2-2}$` distribution:

`$$T = \frac{V - v_0}{s_p\sqrt{1/n_1 + 1/n_2}} \sim t_{n_1 + n_2 - 2}$$`

---

**Scenario 2**: `$\sigma_1^2 \neq \sigma_2^2$`.

In this case, we do not gain any insights, and so there's no adjustments we can make to the test statistic.

It turns out that

`$$T = \frac{V - v_0}{\sqrt{s_1^2/n_1 + s_2^2/n_2}} \sim t_{\nu},$$`

where

$$
  \nu = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} \right)^2}{\frac{(s_1^2/n_1)^2}{n_1-1} + \frac{(s_2^2/n_2)^2}{n_2-1}}
$$

In either case, we can find the distribution of `$T$`, and use this to either reject or not reject the null hypothesis!

---

Since we do not know `$\sigma_1^2$` or `$\sigma_2^2$`, we use `$s_1^2$` and `$s_2^2$` to determine if we find it plausible that `$\sigma_1^2 = \sigma_2^2$`.

The general rule of thumb: if `$0.5 < \frac{s_1}{s_2} < 2$`, then we are okay with assuming `$\sigma_1^2 = \sigma_2^2$`.

In our lizards example:

```r
std_devs <- lizards %>% 
  group_by(group) %>% 
  summarize(s = sd(size),
            n = n())

std_devs
```

```
## # A tibble: 2 x 3
##   group     s     n
##   <chr> <dbl> <int>
## 1 alive  2.76    12
## 2 dead   2.22    10
```

So, we will assume `$\sigma_\text{dead}^2 = \sigma_\text{alive}^2$`.

---

That means we have to find `$s_p^2$` for our test:

```
sp2 <- ((12 - 1)*2.7607339^2 + (10 - 1)*2.2212872^2)/(12 + 10 - 2)
sp2
```

```
## [1] 6.412261
```

We can now calculate the observed value of the test statistic:

.pull-left[

```r
means_and_ns <- lizards %>% 
  group_by(group) %>% 
  summarize(means = mean(size),
            n = n())
means_and_ns
```

```
## # A tibble: 2 x 3
##   group means     n
##   <chr> <dbl> <int>
## 1 alive  23.2    12
## 2 dead   20.8    10
```
]

.pull-right[
$$
`\begin{aligned}
T_\text{obs} &= \frac{V - v_0}{\widehat{SD}(V)} \\
             &= \frac{\bar{X}_\text{alive} - \bar{X}_\text{dead}}{s_p\sqrt{1/n_\text{alive} + 1/n_\text{dead}}} \\
             &= \frac{23.1616667 - 20.785}{2.5322442\sqrt{1/12 + 1/10}} \\
             &= 2.1920072
\end{aligned}`
$$
]

---

We compare this to a `$t_{n_\text{alive} + n_\text{dead} - 2}$` distribution to find the p-value:

---

We compare this to a `$t_{n_\text{alive} + n_\text{dead} - 2}$` distribution to find the p-value:

```r
T_20 <- StudentsT(20)
2*(1 - cdf(T_20, 2.192))
```

```
## [1] 0.04038106
```

---

```r
t.test(data = lizards,
       size ~ group, var.equal = TRUE)
```

```
## 
## 	Two Sample t-test
## 
## data:  size by group
## t = 2.192, df = 20, p-value = 0.04038
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.1149771 4.6383563
## sample estimates:
## mean in group alive  mean in group dead 
##            23.16167            20.78500
```

---

Which decade had better movies: the 90s of 2010s?

```r
movies_orig <- read_csv('https://raw.githubusercontent.com/idc9/stor390/master/data/movies.csv')
movies <- movies_orig %>% 
  mutate(decade = as.numeric(str_sub(thtr_rel_year, start = 3, end = 3))*10)

DT::datatable(movies, options = list(pageLength = 3, scrollX = TRUE))
```

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com/m/body_of_evidence/","//www.rottentomatoes.com/m/the_hunger_games/","//www.rottentomatoes.com/m/hells_kitchen_nyc/","//www.rottentomatoes.com/m/lake_house/","//www.rottentomatoes.com/m/in_the_name_of_the_father/","//www.rottentomatoes.com/m/desperate_measures/","//www.rottentomatoes.com/m/invasion/","//www.rottentomatoes.com/m/eye_of_the_needle/","//www.rottentomatoes.com/m/funny_lady/","//www.rottentomatoes.com/m/1184827-alvin_and_the_chipmunks/","//www.rottentomatoes.com/m/pina_3d/","//www.rottentomatoes.com/m/1151898-capote/","//www.rottentomatoes.com/m/dead_men_dont_wear_plaid/","//www.rottentomatoes.com/m/tarzan/","//www.rottentomatoes.com/m/cocoon_the_return/","//www.rottentomatoes.com/m/death_defying_acts/","//www.rottentomatoes.com/m/half_baked/","//www.rottentomatoes.com/m/1203339-dance_of_the_dead/","//www.rottentomatoes.com/m/around_the_world_in_80_days/","//www.rottentomatoes.com/m/lol_2011/"],[10,0,90,90,0,0,80,90,10,10,80,90,0,0,80,0,90,90,0,0,90,0,10,90,0,80,90,10,80,80,10,0,90,90,0,10,0,90,80,80,0,70,0,0,80,80,90,0,70,90,0,0,0,0,90,90,0,90,10,80,90,0,0,0,0,10,80,80,80,70,0,0,90,70,80,0,10,0,90,90,90,80,90,0,10,10,0,90,80,80,10,80,10,0,80,80,80,90,70,0,10,80,90,90,0,10,0,0,80,90,10,80,0,0,90,0,10,90,90,10,90,0,0,0,70,0,10,10,0,10,90,90,10,80,80,90,90,10,0,0,70,70,70,10,70,80,70,0,90,90,0,0,10,90,10,80,90,0,0,10,80,90,80,0,0,0,90,0,70,80,90,90,90,10,0,0,0,0,90,0,80,0,70,80,90,90,0,0,80,0,10,90,90,0,90,0,80,0,90,10,0,0,90,10,0,90,80,0,70,90,90,90,80,80,10,0,70,90,0,80,10,0,90,0,10,0,90,10,0,0,0,10,80,90,80,90,0,0,90,0,10,90,90,0,0,0,0,90,0,0,90,70,90,10,90,90,0,10,0,10,80,90,0,0,70,90,0,90,80,70,0,90,90,0,0,0,70,0,90,70,80,80,80,0,0,90,0,80,80,70,0,0,10,10,0,0,90,90,0,80,10,10,90,90,0,0,10,0,10,10,80,90,0,80,90,80,90,80,0,0,80,0,0,0,10,0,80,10,0,0,90,80,90,0,90,0,90,10,10,10,90,80,90,10,80,80,0,0,0,10,0,70,70,90,90,80,70,0,10,10,10,10,90,0,90,90,80,90,0,0,90,10,90,90,80,0,80,10,70,90,10,0,10,0,80,0,90,70,0,0,70,10,0,10,0,0,10,90,10,70,70,70,90,80,0,90,70,0,0,70,0,0,10,90,70,0,0,80,0,90,0,0,0,0,70,80,10,0,0,0,10,10,90,0,80,80,70,10,90,70,70,90,90,80,0,80,10,90,10,10,70,70,10,10,90,0,90,80,90,90,0,10,80,90,0,0,10,0,90,0,0,0,0,90,0,0,0,0,0,0,80,0,0,90,80,0,90,90,90,90,0,0,80,0,0,0,90,10,10,0,0,0,80,80,80,0,80,90,70,10,90,90,90,0,0,10,90,0,80,0,70,0,70,0,90,10,0,90,70,80,10,10,10,0,0,70,90,80,90,0,90,90,0,80,0,0,0,0,0,80,90,0,10,0,0,80,80,0,0,10,0,0,90,0,90,0,10,10,0,70,90,90,90,0,0,0,0,70,0,80,80,80,80,0,90,0,70,90,80,0,0,10,70,90,0,80,90,90,80,0,10,0,80,70,10,90,0,0,10,90,10,10,0,90,70,0,90,90,90,80,80,90,10,80,90,10,80,90,0,0,0,90,10,90,0,90,90,0,80,70,0,10,0,80,90,80,0,90,0,0,10]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>title<\/th>\n      <th>title_type<\/th>\n      <th>genre<\/th>\n      <th>runtime<\/th>\n      <th>mpaa_rating<\/th>\n      <th>studio<\/th>\n      <th>thtr_rel_year<\/th>\n      <th>thtr_rel_month<\/th>\n      <th>thtr_rel_day<\/th>\n      <th>dvd_rel_year<\/th>\n      <th>dvd_rel_month<\/th>\n      <th>dvd_rel_day<\/th>\n      <th>imdb_rating<\/th>\n      <th>imdb_num_votes<\/th>\n      <th>critics_rating<\/th>\n      <th>critics_score<\/th>\n      <th>audience_rating<\/th>\n      <th>audience_score<\/th>\n      <th>best_pic_nom<\/th>\n      <th>best_pic_win<\/th>\n      <th>best_actor_win<\/th>\n      <th>best_actress_win<\/th>\n      <th>best_dir_win<\/th>\n      <th>top200_box<\/th>\n      <th>director<\/th>\n      <th>actor1<\/th>\n      <th>actor2<\/th>\n      <th>actor3<\/th>\n      <th>actor4<\/th>\n      <th>actor5<\/th>\n      <th>imdb_url<\/th>\n      <th>rt_url<\/th>\n      <th>decade<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"pageLength":3,"scrollX":true,"columnDefs":[{"className":"dt-right","targets":[4,7,8,9,10,11,12,13,14,16,18,33]},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[3,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>

---

We'll use `critics_score` as our criteria for "good movie". This dataset contains a random sample of movies from IMDB.

We will test `$H_0: \mu_{90} = \mu_{10}$` against `$H_A: \mu_{90} \neq \mu_{10}$` using `$\alpha = 0.01$`.

First, need to find out if we can assume equal variances:

```r
movies %>% 
  group_by(decade) %>% 
  summarize(s = sd(critics_score))
```

```
## # A tibble: 5 x 2
##   decade     s
##    <dbl> <dbl>
## 1      0  28.4
## 2     10  27.1
## 3     70  25.3
## 4     80  28.0
## 5     90  28.8
```

We can!

---

So, let's find means, `$s_p$`, and `$T_\text{obs}$`.

.pull-left[

```r
movies %>% filter(decade %in% c(90, 10)) %>% 
  group_by(decade) %>% 
  summarize(means = mean(critics_score),
            s = sd(critics_score),
            n = n())
```

```
## # A tibble: 2 x 4
##   decade means     s     n
##    <dbl> <dbl> <dbl> <int>
## 1     10  62.4  27.1   102
## 2     90  52.9  28.8   161
```

```r
sp2 <- ((102 - 1)*27.1^2 + (161 - 1)*28.79^2)/(102 + 161 - 2)
sp2
```

```
## [1] 792.3129
```
]

.pull-right[

$$
`\begin{aligned}
  T_\text{obs} &= \frac{V - v_0}{\widehat{SD}(V)} \\
               &= \frac{\bar{x}_{10} - \bar{x}_{90}}{s_p \sqrt{1/n_{10} + 1/n_{90}}} \\
               &= \frac{62.42 - 52.88}{\sqrt{792.31} \sqrt{1/102 + 1/161}} \\
               &= 2.6781565
\end{aligned}`
$$
]

---

**If** `$H_0$` is true, `$T \sim t_{n_{10} + n_{90} - 2}$`.

---

Since we are testing against `$H_A: \mu_{90} \neq \mu_{10}$`, we need to consider both tails:

---

```
T_261 <- StudentsT(261)

2*(1-cdf(T_261, 2.6781565))
```

```
## [1] 0.00787261
```

Since the p-value is smaller than `$\alpha$`, we reject the null hypothesis. There seems to be a difference in mean critic score between 1990s movies and 2010s movies.

The quick way:

```r
t.test(data = filter(movies, decade %in% c(10, 90)),
       critics_score ~ decade, var.equal = TRUE)
```

```
## 
## 	Two Sample t-test
## 
## data:  critics_score by decade
## t = 2.6796, df = 261, p-value = 0.007839
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   2.531214 16.560371
## sample estimates:
## mean in group 10 mean in group 90 
##         62.42157         52.87578
```

---

Concrete used for roadways or buildings is often reinforced with a material that is placed inside the setting concrete. A common example of this is called ’rebar’ which is short for ’reinforcing bar’ and is usually made out of steel. You can often see rebar poking out of the concrete of demolished buildings. It is desireable that the reinforcing material is strong and corrosion resistant. Steel is strong, but tends to corrode over time, so experiments were conducted to test two corrosion resistant materials, one made of fiberglass and the other made of carbon.

Eight beams with fiberglass reinforcement, and 11 beams with carbon reinforcement were poured, and each was then subjected to a load test, which measures the strength of the beam. Strength is measured in kN (kiloNewtons), which is a measure of the force required to break the beam.

Research question: is there any difference in strength?

I.e., want to test `$H_0: \mu_\text{fiber} = \mu_\text{carbon}$` vs. `$H_A: \mu_\text{fiber} \neq \mu_\text{carbon}$`.

(Or, equivalently, `$H_0: \mu_\text{fiber} - \mu_\text{carbon} = 0$` vs. `$H_0: \mu_\text{fiber} - \mu_\text{carbon} \neq 0$`.)

---

```r
DT::datatable(rebars, options = list(pageLength = 5))
```

<div id="htmlwidget-9cca16fba2f4933cf42c" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-9cca16fba2f4933cf42c">{"x":{"filter":"none","data":[["1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19"],["fiberglass","fiberglass","fiberglass","fiberglass","fiberglass","fiberglass","fiberglass","fiberglass","carbon","carbon","carbon","carbon","carbon","carbon","carbon","carbon","carbon","carbon","carbon"],[38.3,29.6,33.4,33.6,30.7,32.7,34.6,32.3,48.8,38,42.2,45.1,32.8,47.2,50.6,44,43.9,40.4,45.8]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>type<\/th>\n      <th>strength<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"pageLength":5,"columnDefs":[{"className":"dt-right","targets":2},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[5,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>

---

.pull-left[

```r
ggplot(rebars,
       aes(x = type, y = strength)) + 
  geom_boxplot() +
  geom_jitter(width = 0.2, height = 0,
              aes(color = type)) +
  geom_hline(data = rebars %>% 
               group_by(type) %>% 
               summarize(means = mean(strength)),
             aes(yintercept = means,
                 color = type)) + 
  theme(legend.position = "bottom")
```
]

.pull-right[
<img src="data:image/png;base64,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" width="300px" height="500px" style="display: block; margin: auto;" />
]

---

First, need to decide if we can assume equal variances:

.pull-left[

```r
rebars %>% 
  group_by(type) %>% 
  summarize(s = sd(strength))
```
]

.pull-right[

```
## # A tibble: 2 x 2
##   type           s
##   <chr>      <dbl>
## 1 carbon      5.06
## 2 fiberglass  2.63
```
]

Since the standard deviation of the strength of carbon bars is more than twice that of the fiberglass bars, we cannot assume that the variances are the same!

---

The simple step first: find the observed test statistic:

```r
rebars %>% 
  group_by(type) %>% 
  summarize(means = mean(strength),
            s = sd(strength),
            n = n()) %>% print() %>% # code for first table ends here
  ungroup() %>% 
  summarize(T_obs = diff(means)/(sqrt(sum(s^2/n))))
```

```
## # A tibble: 2 x 4
##   type       means     s     n
##   <chr>      <dbl> <dbl> <int>
## 1 carbon      43.5  5.06    11
## 2 fiberglass  33.2  2.63     8
```

```
## # A tibble: 1 x 1
##   T_obs
##   <dbl>
## 1 -5.80
```

---

"By hand":

$$
`\begin{aligned}
  T_\text{obs} &= \frac{V - v_0}{\widehat{\text{SD}}(V)} \\
               &= \frac{\bar{x}_\text{fiber} - \bar{x}_\text{carbon}}{\sqrt{s^2_\text{fiber}/n_\text{fiber} + s^2_\text{carbon}/n_\text{carbon}}} \\
               &= \frac{33.15 - 43.53}{\sqrt{2.63^2/8 + 5.06^2/11}} \\
               &= -5.8096699
\end{aligned}`
$$

---

Next, we need to determine the degrees of freedom. Since we cannot assume equal variances, we need to use what is known as Satterthwaite's approximation:

$$
`\begin{aligned}
  \nu &= \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} \right)^2}{\frac{(s_1^2/n_1)^2}{n_1-1} + \frac{(s_2^2/n_2)^2}{n_2-1}} \\
      &= \frac{\left(\frac{2.63^2}{8} + \frac{5.06^2}{11} \right)^2}{\frac{(2.63^2/8)^2}{8-1} + \frac{(5.06^2/11)^2}{11-1}} \\
      &= 15.7119324
\end{aligned}`
$$

When used to determine the correct df, we always round down. So, `$\nu = 15$`.

---

So, if `$H_0$` is true, `$T \sim t_{15}$`.

---

Since `$H_A: \mu_\text{fiberglass} \neq \mu_\text{carbon}$`, we find the p-value as twice the area to the left of the observed value:

```
T_15 <- StudentsT(15)
2*cdf(T_15, -5.8096699)
```

```
## [1] 3.43928e-05
```

The p-value is very, very small, so we reject the null hypothesis. It seems that there is a difference in mean strength between the two materials.

---

**Summary**

A Two Sample T-test with Independent Samples uses the test statistic `$T = \frac{V - v_0}{\widehat{\text{SD}}(V)}$`, where `$V = \bar{X}_1 - \bar{X}_2$` and `$v_0$` is the "null value" ( `$H_0: V = v_0$`; usually `$v_0 = 0$` ).

.pull-left[

If `$0.5 < \frac{s_1}{s_2} < 2$`, we assume equal variances `$\sigma_1^2 = \sigma_2^2$`. In this case,

* `$\widehat{\text{SD}}(V) = s_p \sqrt{1/n_1 + 1/n_2}$`, where `$$s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}$$`

* if `$H_0$` is true, `$T \sim t_{n_1 + n_2 - 2}$`. 
]

.pull-right[

If we cannot assume equal variances,

* `$\widehat{\text{SD}}(V) = \sqrt{s_1^2/n_1 + s_2^2/n_2}$`

* if `$H_0$` is true, `$T \sim t_{\nu}$` where `$$\nu = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} \right)^2}{\frac{(s_1^2/n_1)^2}{n_1-1} + \frac{(s_2^2/n_2)^2}{n_2-1}}$$`
]

---
layout: true

# Two Independent Sample T Confidence Interval

---

As always, simply performing a test does not give us a lot of information. It simply answers the question "is this one value plausibly the true value?", where we would much rather ask "what values could be the true value?"

Fortunately, we can construct confidence intervals for the difference in means from the two sample t-test.

1. Find the distribution of `$T = \frac{V - v_0}{\widehat{\text{SD}}(V)}$` **assuming** the null hypothesis is true.

2. Find cut-offs (i.e. quantiles) in said distribution such that we have `$\alpha$` outside the cut-offs.

3. Create the confidence interval as `$V_\text{obs} \pm t_{\text{df}, \alpha/2} \widehat{\text{SD}}(V)$`.

---

**Example: Fiber vs Carbon**

We already established that the variances are not equal, and found `$\nu = 15$`. So, we can find a `$90\%$` CI as follows:

.pull-left[

```r
rebars %>% 
  group_by(type) %>% 
  summarize(mean = mean(strength),
            s = sd(strength),
            n = n())
```

```
## # A tibble: 2 x 4
##   type        mean     s     n
##   <chr>      <dbl> <dbl> <int>
## 1 carbon      43.5  5.06    11
## 2 fiberglass  33.2  2.63     8
```

```r
quantile(T_15, 1-0.1/2)
```

```
## [1] 1.75305
```

]

.pull-right[
.small[
$$
`\begin{aligned}
  V_\text{obs} &\pm t_{15, 0.1/2}\widehat{\text{SD}}(V) \\
  &= \bar{X}_\text{fiber} - \bar{X}_\text{carbon} \pm t_{15, 0.1/2} \sqrt{\frac{s^2_\text{fiber}}{n_\text{fiber}} + \frac{s^2_\text{carbon}}{n_\text{carbon}}} \\ 
  &= 33.15 - 43.53 \pm 1.75 \sqrt{2.63^2/8 + 5.06^2/11} \\
  &= -10.38 \pm 3.13
\end{aligned}`
$$
]

So the 90% CI for the difference in means is [-13.51, -7.25].
]

---

**Example: IMDB Movies**

We saw that we can reasonably assume equal variances, and found the pooled variance. We can now find a `$99\%$` CI.

.pull-left[

```r
movies %>% 
  filter(decade %in% c(90, 10)) %>% 
  group_by(decade) %>% 
  summarize(means = mean(critics_score),
            s = sd(critics_score),
            n = n())
```

```
## # A tibble: 2 x 4
##   decade means     s     n
##    <dbl> <dbl> <dbl> <int>
## 1     10  62.4  27.1   102
## 2     90  52.9  28.8   161
```

```r
((102-1)*27.1^2 + (161-1)*28.8^2)/(102 + 161 - 2)
```

```
## [1] 792.6659
```
]

.pull-right[

```r
quantile(T_261, 1 - 0.01/2)
```

```
## [1] 2.594797
```

.small[
$$
`\begin{aligned}
  V_\text{obs} &\pm t_{261, 0.01/2}\widehat{\text{SD}}(V) \\
  &= \bar{X}_\text{10} - \bar{X}_\text{90} \pm t_{261, 0.01/2} \sqrt{s_p^2 \left(\frac{1}{n_\text{10}} + \frac{1}{n_\text{90}}\right)} \\ 
  &= 62.4 - 52.9 \pm 2.59 \sqrt{792.31\cdot (1/102 + 1/161)} \\
  &= 9.5 \pm 9.23
\end{aligned}`
$$
]

So the 99% CI for the difference in means is [0.27, 18.73].
]